You definitely have to protect yourself from the cold temperatures of the mud, and especially water! In terms of the cleanup water and watery mud, here is an example of what to expect. In mid October I prepare a number of plants in my garden pond for the winter, and sometimes I have to stand in it to get at some things (also in March/April when I am setting things up for the new season). I put on layers of jackets to try and compensate for what my legs/feet are going to experience. When my legs hit the water (18 inches deep), I feel intense pain, and feel light-headed and dizzy, almost like I am going to pass out!

I feel like I just want to squirm out of my skin!

After a while, my legs eventually lose their feeling, and I can finish the in-pond work (I go in barefoot because I need to be certain I am not stepping on some sharp debris that could puncture the liner). After I get out and warm up, the circulation starts up in my legs again, and rest of my body is suddenly infused with ice-cold blood, making me even more chilled! A good hot shower helps! And all that is from exposing only my lower calves to 18 inches of water, while the rest of my body is heavily clothed and dry! Hope that convinces you to protect yourself from the cold water/mud!
Thick mud may get a layer of warmer mud where it contacts your skin from absorbing your body heat and not dissipating it away as quickly as water, but at this time of year that warmup (relatively speaking) would be insufficient, and you would still get dangerously chilled! If you get stuck in quicksand that packed around you, or the suction of thick mud gets your footwear stuck, then things can turn downright dangerous, or deadly!
I know that this mild El Nino winter makes it feel like spring, but don't kid yourself! Until the sun gets a bit higher and the daylength a bit longer, it is still winter! When you mentioned that your feet were sinking into the soil a tad, that meant that the surface of the ground is thawing, but it is likely frozen deeper down. We had a frigid December with little snow, causing the ground to freeze to a much greater depth! In fact, a week ago, our vegetable garden was a quagmire, where I would sink down a few inches with each step! But the extra muddiness was because it was still frozen a few inches down, and the water in the soil couldn't drain away until the frozen layer deeper down thawed. So, for a while, the garden was like a 3-inch layer of softened chocolate! So, chances are that much mud would be very shallow, with it frozen just below the surface.
But, exceptions are springs, where groundwater can keep things thawed, or perhaps along river banks, where flowing water has kept things from freezing, or reduced the amount of freezing (springs can be there as well).
Just a shot in the dark, perhaps a thin layer of saturated soil overtop frozen ground could slip down a steep enough slope, and accumulate into a deeper mass. The Alberta Badlands therefore could be such a place where theoretically that situation might present itself, but I am just making an educated guess, never having been there.
For rivers, you could try checking out this one that goes through the center of the screen:
http://maps.google.com/maps?t=h&hl=en&i ... 87111&z=12 Zoom in, scroll around, find roads to access parts of it, and remember, play safe! Hypothermia is your enemy!
Hope this helps!
